It’s called a sinusoidal grating because the grayscale values vary according to the sine function.
If you plot the values along a horizontal line of the grating, you’ll get a plot of a sine function
Sinusoidal gratings can have different orientations…
…and different frequencies—these are spatial frequencies, not temporal ones
There's one more parameter that defines a sinusoidal grating: the phase. Gratings with a different phase are shifted with respect to each other…
Or even better, you can use a function of both x and y to make any grating
And therefore, you can reconstruct the image by adding all of those sinusoidal gratings together.
The more gratings you add, the closer the result is to the actual image
Here's another example
and another one…
There's a lot more than can fit in a single thread.
If you want to read more detail, and go through the step-by-step writing of the code to decompose & recostruct *any* image, read full article here:
So, this thread could serve as my my #introduction
I'm Stephen. I used to be a physicist (as you can guess from the thread above) but now I focus on communicating about Python and programming and teaching coding
You can expect more varied content from me, all related to #programming in #Python, from science-y stuff like this, to fun animations using the `turtle` module (no not those boring ones!) and general Python for those learning to code at beginner and intermediate levels
Not sure whether you’re only meant to get a single shot at an #introduction, but I’ll extend on mine a bit now that I’m starting to find my feet here
However, my first career was as a physicist
Most of my science work centred around novel retinal imaging technology with the primary aim of early disease diagnosis, plus a bit more about the optics of the eye.
I learnt to code as part of my PhD work and then relied on programming (mostly MATLAB, at the time, before the Python-era) for all of my research work, from simulation and modelling, to running the lab experiments, to analysing the data.
When I left academia, I decided to focus on teaching programming to both children and adults.
I spend a lot of time creating learning content, including The Python Coding Book and regular articles on the blog.
I also run codetoday which runs live lessons for children from age 7 to learn coding in Python (only Python, no kids-platforms. Yes, starting from age 7, you’d be surprised how well they pick the basics up)
I’ll be sharing bits on content regularly here too, typically aimed at intermediate learners (including those aiming to move from beginners to intermediate), including steering towards scientific programming and related fields.
OK, I’ve abused #QOTO’s longer character limit too much, so I’d better stop!
@s_gruppetta In my 35 years as a sotfware engineer I have seen a lot of code that looks like it was written by seven year olds. 😆
@s_gruppetta Would it be feasible to include the code in the toot or as alt text? I'd love to try pasting it into Python, but of course I can't do that from an image.
@peterdrake I have been doing this (on Twitter) for a few months now, but this is an old post (from Twitter, recycled here) so the images didn’t have them. I now autogenerate these snippets which makes adding the code in ALT text easy
@s_gruppetta this is so cool! I am intimately familiar with Fourier series for time series analysis and dynamical systems, but for some reason never connected the dots to images (pun intended). Thanks for sharing!
@mattkram Thank you! In a previous life, I was an optical physicist, so for me, the Fourier Transform is in 2D first and foremost, and for spatial data. When I see 1D Fourier transforms in the temporal domain I need to readjust!
A lens is a real-life Fourier transform calculator, after all!
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